We just went through something like this, but never got around to trying a nebulizer. My 3 year old caught a cough, but it had not really gone away after 5-6 weeks. He continued with this minor annoying cough that was"wet". I took him in and the MD did a chest x-ray. The lungs did not look completely clear to her but he also had some nasal irritation. So she did 2 things...put him on antibiotics and recommended Children's Zytec for allergies. So I used both. By about the 2nd day his cough was almost gone. By the end of the antibiotics it was completely gone. A couple times since then he has been coughing, especially while nap and night time, so I have given him the Zyrtec and that has stopped it. The MD recommended giving the Zyrtec at night since it can make your child sleepy. I did find out later that the Radiologist who looked at the x-rays later said the lungs were clear and there were no pneumonia. But I do believe there was some type of mild infection. I hate to give anyone medicine, but in this case it really saved the day. I had not thought my son was still under the weather until he was treated and I realized he really had not been completely himself.
Good luck, I hope you get this figured out!